1. Field of the Invention
The present invention relates to a phase difference detector for computing the phase difference between two alternating current signals (AC signals) having the same frequency. The invention also relates to a program for detecting such a phase difference, and to a plasma processing apparatus utilizing such a phase difference detector.
2. Description of the Related Art
Conventionally, a digital computation technique has been known for determining the phase difference between two AC signals of the same frequency. For instance, Japanese Patent No. 3808973 discloses the following method for computing the phase difference between two AC signals: s1=A1·cos(ω·t) and s2=A2·cos(ω+t+φ), where ω=2π·f, f represents frequency, and φ represents a phase difference from the signal s1.    (1) A sine (or sinusoidal) wave s3=cos((ω+ωo)·t), ωo=2·π·fo, having a frequency of (f+fo)[Hz] (fo<<f) is generated by using a direct digital synthesizer. Then, the sine wave is multiplied by each of the AC signals s1 and s2, whereby the following signals sa and sb are obtained.
                                          s            a                    =                    ⁢                                    s              1                        ×                          s              3                                                                    =                    ⁢                                    A              1                        ·                          cos              ⁡                              (                                  ω                  ·                  t                                )                                      ·                          cos              ⁡                              (                                                      (                                          ω                      +                                              ω                        o                                                              )                                    ·                  t                                )                                                                                  =                    ⁢                                    (                                                A                  1                                /                2                            )                        ·                          [                                                cos                  ⁡                                      (                                                                  (                                                                              2                            ⁢                            ω                                                    +                                                      ω                            o                                                                          )                                            ·                      t                                        )                                                  +                                  cos                  ⁡                                      (                                                                  ω                        o                                            ·                      t                                        )                                                              ]                                                                                    s            b                    =                    ⁢                                    s              2                        ×                          s              3                                                                    =                    ⁢                                    A              2                        ·                          cos              ⁡                              (                                  ω                  +                  t                  +                  ϕ                                )                                      ·                          cos              ⁡                              (                                                      (                                          ω                      +                                              ω                        o                                                              )                                    ·                  t                                )                                                                                  =                    ⁢                                    (                                                A                  2                                /                2                            )                        ·                                          [                                                      cos                    ⁡                                          (                                                                        (                                                                                    2                              ⁢                              ω                                                        +                                                          ω                              o                                                        +                            ϕ                                                    )                                                ·                        t                                            )                                                        +                                      cos                    ⁢                                          (                                                                                                    ω                            o                                                    ·                          t                                                +                        ϕ                                            )                                                                      ]                            .                                              (2) Filtering is performed with respect to the signals sa and sb to remove frequency components higher than fo, thereby extracting low frequency signals sa(A1/2)·cos(ω·t) and sbo=(A2/2)·cos(ω·t+φ) having the frequency fo.    (3) The two low frequency signals sao and sbo are transformed into rectangular waves, and by using the reference clock of a direct digital synthesizer, the period T(=1/fo) and the deviation time t of the rise timings of the two low frequency signals sao, sbo are obtained. By computing 360×(t/T)[°] or 2π×(t/T)[rad], the phase difference φ is obtained.
In the above technique for computing phase difference disclosed in U.S. Pat. No. 3,808,973, after detected values of two AC signal s1 and s2 having a phase difference φ are converted into low frequency signal sao and sbo, the period T and the deviation time t of the rise timings of the two low frequency signals sao and sbo are measured by using a clock of a reference clock, and then the measured values are used to obtain the phase difference φ.
When the frequency of the reference clock is fCLK, the period τ of the reference clock is τ=1/fCLK, and the period T of the low frequency signals sao, sbo is T=1/fo. Thus, the resolving power N for measuring the period T is N=T/τ=fCLK/fo[times/period]. When the resolving power N is converted into a resolving power B in terms of angle, B=360/N=360×fo/fCLK[°] or B=2π×fo/fCLK[rad]. In this way, since the phase difference φ is computed by using the period T and the phase deviation time t of the low frequency signals sao, sbo in the conventional phase difference computation method, the accuracy of the computation results depends on the resolving power B.
Specifically, when the ratio of the frequencies Rf=fo/fCLK is increased, the resolving power B increases, which results in lower detection accuracy. When the ratio Rf is decreased, the resolving power B decreases, which results in higher detection accuracy. Thus, to improve the detection accuracy, it may be considered to set the value of the frequency fCLK of the reference clock high or to set the value of the frequency fo low. However, since the speed of a device such as a direct digital synthesizer that uses a reference clock for operation or a counter for measuring the period T or the phase deviation time t cannot be increased beyond a certain limit, the frequency fCLK cannot be set to a high value as desired.
On the other hand, since the phase difference φ is detected at the period T=1/fo, setting the frequency fo low leads to long detection intervals. Thus, in the case where the phase difference φ changes largely when detection is not being performed, the reliability of the detected value is low.
In this way, in the conventional phase difference detection method, the resolving power B depends on the ratio Rf=fo/fCLK and the detection period (1/fo) is a trade-off for the resolving power B (detection accuracy), so that it is difficult to set optimum values for the frequency fo and the frequency fCLK of the reference clock.